Question

Which term of the AP 53, 48, 43,....................... is the first negative term.?

Answer 1

53, 48, 53..........

First term or 'a' = 53

Common difference or 'd' = 48 - 53 = - 5

Let nth term is the first negative term of the given AP.

Now,

nth term in AP = a + (n - 1)*d

= 53 + (n -1)*(- 5)

= 53 - 5n + 5

= 53 + 5 - 5n

= 58 - 5n

Now, we have to find the suitable value of n, so that the value of (58 - 5n) is negative.

Let us take n = 11

nth term = 58 - (5*11)

= 58 - 55

= 3

Which is not negative.

Now, putting n = 12, we get.

nth term = 58 - (5*12)

= 58 - 60

= - 2

This is the first negative term of the series and it is the 12th term of the AP.

So, n =12